Two-stage CCI/ISI reduction with space-time processing in TDMA cellular networks

ABSTRACT

A two-stage, space-time digital receiver provides improved estimates of data symbols from a received signal comprising the data symbols, co-channel interference, and intersymbol interference. The first stage uses a space-time linear filter to process the received signal and provide an intermediate signal with substantially reduced co-channel interference content and substantially unaltered intersymbol interference content relative to that of the received signal. The second stage uses a Viterbi equalizer to estimate the data symbols from the intermediate signal. Because the receiver performs Viterbi equalization on the intermediate signal with reduced co-channel interference, its performance is superior to that of receivers that directly Viterbi equalize the received signal. A first embodiment of a receiver according to the present invention determines the weight coefficient matrix for the linear filter by applying MMSE criteria to the error between the intermediate signal and a reference signal derived from the convolution of known training symbols with a first set of estimated channel vectors. The first embodiment also derives a second set of estimated channel vectors from the intermediate signal for the Viterbi equalizer. A second embodiment jointly determines the coefficients for the linear filter and estimated channel vector for the Viterbi equalizer, respectively, by maximizing a single SINR objective function.

This application claims priority from U.S. Provisional PatentApplication 60/064,352 filed Nov. 4, 1997, which is incorporated hereinby reference.

This invention was supported by the Department of the Army undercontract DAAH04-95-I-0436. The U.S. Government has certain rights in theinvention.

FIELD OF THE INVENTION

This invention relates to receiving an information signal in a TimeDivision Multiple Access cellular network, and, in particular, to atwo-stage space-time digital signal processing method and apparatus forreducing both co-channel interference and intersymbol interference in areceived signal to obtain the information signal.

BACKGROUND OF THE INVENTION

In recent years, the use of cellular networks for wirelesscommunications has grown tremendously. In a cellular network, multiplewireless users within a designated area, or cell, communicate with asingle base-station. In a Time Division Multiple Access (TDMA) cellularnetwork, each user communicates with the base-station in atime-multiplexed fashion. In other words, each user is allocated a sliceof time (i.e., a TDMA time slot) during which it exchanges a burst (orpacket) of data with the base-station. A burst is a sequence of digitalsymbols representing the data. The user must then wait until the otherusers have exchanged their bursts of data with the base-station beforeexchanging its next burst of data.

The quality of communication in a cellular network, often expressed asbit-error-rate (BER), can be degraded by a variety of factors. Threeimportant factors that degrade the quality of communication and increaseBER are multipath fading, noise (e.g., thermal noise), and interference.

There are essentially two types of multipath fading. Flat fading resultswhen the primary ray of the transmitted signal arrives at the receiverat approximately the same time as one or more reflections of thetransmitted signal. If the primary ray and the reflections havedifferent amplitudes and phases, they combine at the reciever in amanner that produces variations in the received signal strength. Thesevariations can include drops in signal strength over several orders ofmagnitude. When there are a large number of reflections, as is often thecase in an urban cellular network with many sources for reflection(e.g., buildings), flat fading produces a Rayleigh distribution. Timedispersion is a second type of multipath fading that occurs when thereflections arrive at the receiver delayed in time relative to oneanother (i.e., their propagation paths have substantially differentlengths). If the relative time delays are a significant portion of asymbol period, then intersymbol interference (ISI) is produced, whereinthe received signal simultaneously contains information from severalsuperimposed symbols. Thus, both types of multipath fading can corruptthe received signal at the receiver.

In addition to multipath fading, noise, such as thermal noise in theanalog front end of a receiver, can also corrupt the received signal atthe receiver. Noise typically has a white frequency distribution (e.g.,constant energy at all frequencies) and a gaussian temporaldistribution, leading to the term additive, white, guassian noise(AWGN).

The third factor that can corrupt the received signal at the receiver isco-channel interference (CCI). CCI is the result of receiving thedesired signal along with other signals which were transmitted fromother radios but occupy the same frequency band as the desired signal.There are many possible sources of CCI. For example, an indirect sourceof CCI is adjacent channel interference (ACI). ACI is the result ofside-band signal energy from radios operating at neighboring frequencybands that leaks into the desired signal's frequency band. A more directsource of CCI is signal energy from other radios operating at the samefrequency band as the desired signal. For example, a cellular radio in adistant cell operating at the same frequency can contribute CCI to thereceived signal in the cell of interest.

All of these sources of signal corruption, but especially CCI and ISI,can significantly degrade the performance of a wireless receiver in aTDMA cellular network. Furthermore, tolerance to CCI determines thefrequency reuse factor and therefore the spectral efficiency(Erlang/Hertz/Basestation) of the cellular network. Since receivedsignals in a wireless system such as a TDMA cellular network typicallycomprise desired symbols as well as CCI, ISI, and noise, successfuldesign of a wireless system requires solutions that address all theseproblems.

The problem of flat or Rayleigh fading can be addressd by implementing areceiver with two or more physically separated antennas and employingsome form of spatial diversity combining. Spatial diversity takesadvantage of the fact that the fading on the different antennas is notthe same. Spatial diversity can also address interference by coherentlycombining the desired signal (i.e., desired symbols) from each antennawhile cancelling the interfering signal (i.e., interfering symbols) fromeach antenna.

CCI differs from ISI in several aspects. First, the energy of CCI can besignificantly lower than the energy of ISI due to larger exponentialdecay of the (usually) longer CCI propagation paths. This imbalance ofenergy causes algorithms designed to simultaneously reduce both CCI andISI to combat ISI more than CCI. Second, in order to remove ISI, thedesired user's channel impulse response must be estimated. This channelimpulse response characterizes the ISI of the desired user's propagationchannel. However, CCI contributes interfering, undesired symbols intothe received signal. Because these interfering symbols can mask thestructure of the ISI, channel estimation in the presence of CCI could beinaccurate. Third, CCI and ISI have different characteristics in thespatial and temporal domains (i.e., angles of arrival and channelimpulse responses). These three differences between CCI and ISI can beutilized to separate and remove them from the desired symbols in thereceived signal.

The optimal theoretical solution to the CCI and ISI problems is areceiver that employs diversity combining and a multi-channelmaximum-likelihood-sequence-estimator (MLSE) equalizer wherein theindividual channel vectors (i.e., the discrete-time channel impulseresponses) are known for all signals (i.e the desired signal and all itsreflections and all the interferers). The MLSE receiver jointlydemodulates both the desired and undesired signals. However, in apractical cellular network, the channels for the CCI are either unknownor can be only approximately determined. Furthermore, in certain casesCCI could have different modulation schemes and baud rates, and hence amulti-channel MLSE becomes much more complicated. Therefore, varioussuboptimal schemes which treat CCI as noise and focus on eliminating ISIwith an equalizer have been proposed. They can be broadly classified asfollows.

One class of receivers use minimum mean-square error (MMSE) criteria toprovide an equalizer that reduces CCI and ISI simultaneously, such asspace-only and space-time MMSE receivers. These receivers are well-knownin the art and are fairly robust to CCI. However, this class ofreceivers implement symbol-by-symbol decision, and therefore, they arenot optimal for ISI which spreads the information content of thereceived signal accross several symbols. Besides, they suffer from noiseenhancement inherent in the MMSE approach due to channel inversion. Thesecond class of receivers that treat CCI as noise use time-only orspace-time minimum mean-square error decision feedback equalizers(MMSE/DFE). This class of receivers can perform adequately at a highsignal-to-interference-plus-noise ratio (SINR). However, catastrophicerror propagation can appear when the CCI is strong or when the receivedsignals are in a deep fade. A third class of receivers that treat CCI asnoise implement MLSE-based algorithms which includespatial-whitening/Viterbi and spatial-temporal-whitening/matchedfilter/Viterbi equalizers. The main advantage of this class of receiversis that they effectively combat ISI without producing noise enhancementor error propagation. However, the covariance matrix of the CCI must beknown. All three classes of receivers described above require eitheraccurate estimation of channel information or the covariance matrix ofCCI plus noise. However, in practical situations, the presence of severeCCI impairs the accuracy of estimation of these parameters, and hencethe receiver performance. It is therefore desirable to provide a digitalreceiver for a TDMA network which provides improved estimation of thedesired symbols in a received signal that includes the desired symbols,CCI, ISI, and noise.

SUMMARY OF THE INVENTION

Accordingly, the present invention provides a method and apparatus for aTDMA digital receiver that provides improved processing of a receivedsignal containing desired symbols, CCI, and ISI. The digital receiveraccording to the present invention uses a two-stage, space-time approachincluding a first-stage linear filter for reducing the CCI in thereceived signal and a second-stage Viterbi equalizer for reducing theISI in the received signal. This receiver structure enables thesecond-stage Viterbi equalizer to provide accurately estimated symbolscorresponding to the desired symbols in the received signal.

A first embodiment of the present invention uses amulti-input-multi-output (i.e., MIMO), space-time, linear,finite-impulse-response (i.e., FIR) filter as its first-stage linearfilter. This MIMO space-time filter utilizes the differences in spatialand temporal characteristics between interferences and signals, such asdifferent angles of arrival, fading parameters, and multipath delayprofile, to effectively remove the CCI from the received signal. Inorder to calculate the optimal filter weight coefficents (i.e., weightmatrix, W) for the MIMO space-time filter, a training sequence isconvolved with a first set of estimated channel vectors to provide areference signal. MMSE criteria are then applied to an error termdefined as the difference between the filter output and the referencesignal. The filter weight coefficients are optimized jointly in thespatial and temporal domains to obtain the full benefit of both spaceand time diversity. The received signal is then filtered by the linearfilter in accordance with the optimal filter weight coefficents toprovide a space-time intermediate signal with suppressed CCI content andsubstantially preserved ISI content relative to that of the receivedsignal.

The first embodiment of the present invention uses a multi-channel,space-time Viterbi equalizer as its second-stage. A second set ofestimated channel vectors is computed from the intermediate signal forthe Viterbi equalizer. Because of the reduced CCI content andsubstantially unaltered ISI content of the intermediate signal, thissecond set of estimated channel vectors is more accurate than the firstset of estimated channel vectors. The space-time Viterbi equalizer thenuses the second set of estimated channel vectors to process theintermediate signal, substantially remove the ISI, and provide estimatesof the desired symbols in the received signal. The multi-channel Viterbiequalizer's branch metric calculation captures the benefit of spatialdiversity.

In a second embodiment of the present invention, a joint optimizerminimizes the influence of CCI on the estimation of the receiverparameters. The joint optimizer solves a closed-form objective functionto jointly determine an optimal space-time weight vector ofcoefficients, W_(opt), for the linear filter and an optimal effectivechannel vector, h_(opt), for the Viterbi equalizer. The linear filter isa multi-input-single-output (i.e., MISO), space-time, linear, FIRfilter, and the Viterbi equalizer is a single-channel Viterbi equalizer.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention will be described with reference to the followingdrawings wherein like numerals refer to like components. The drawingsare provided to illustrate various aspects and embodiments of thepresent invention and are not intended to limit the scope of theinvention.

FIG. 1 is a block diagram of a TDMA cellular radio transmission andreception system incorporating M-antenna diversity reception and adigital receiver according to the present invention;

FIG. 2 is a block diagram of a two-stage digital receiver according to afirst embodiment of the present invention;

FIG. 3 is a structural block diagram of a MIMO space-time linear filterfor use inside a digital receiver according to a first embodiment of thepresent invention;

FIG. 4 is plot of the simulated raw BER performance versuscarrier-to-interference-ratio for a single-stage space-time Viterbiequalizer, a single-stage MMSE linear equalizer, and a two-stage digitalreceiver according to a first embodiment of the present invention;

FIG. 5 is a block diagram of a two-stage digital receiver according to asecond embodiment of the present invention;

FIG. 6 is a structural block diagram of a MISO space-time linear filterfor use inside a digital receiver according to a second embodiment ofthe present invention;

FIG. 7 is plot of the pairwise error probability to the nearest neighborversus carrier-to-interference-ratio for a two-stage digital receiveraccording to a second embodiment of the present invention, with andwithout a whitening filter preceding the second-stage Viterbi equalizer;

FIG. 8 is plot of the simulated raw BER performance versuscarrier-to-interference-ratio for a standard multi-channel Viterbiequalizer; a multi-channel Viterbi equalizer preceded by a spatialwhitening filter; a 1 time tap, two-stage digital receiver according toa second embodiment of the present invention; and a 2 time tap,two-stage digital receiver according to a second embodiment of thepresent invention;

FIG. 9 is plot of the simulated raw BER performance versuscarrier-to-interference-ratio for 1 and 2 time tap, two-stage digitalreceivers according to a second embodiment of the present invention,with and without whitening filters preceding the second-stage Viterbiequalizers.

DETAILED DESCRIPTION

In the following description, detailed explanations of well-knownmethods, devices, and circuits are omitted in order to avoid obscuringthe description of the present invention with unnecessary details.Likewise, mathematical simplifications are taken in order to simplifythe description of the method of the present invention. Thesemathematical simplifications are not meant to limit the applicability ofthe present invention to the simplified cases.

A block diagram of a radio transmission and reception system 1 forexchanging information between a single user and a base-station in afrequency-selective slow Rayleigh fading TDMA cellular network is shownin FIG. 1. System 1 includes a transmitter 10 and a wireless receiver 20for transmitting and receiving the information, respectively. Forsimplicity, the description below assumes transmitter 10 is at the userand receiver 20 is at the base-station. However, this is not necessaryfor the present invention, and use of transmitter 10 at the base-stationand receiver 20 at the user is equally valid.

Transmitter 10 has a digital symbol generator 30, as is well-known inthe art, for receiving an information signal (e.g., a sequence of bitsrepresenting voice data) and generating a sequence of correspondingdigital symbols, {right arrow over (s)}, for each TDMA time slot. Thesequence, {right arrow over (s)}, is composed of individual datasymbols, {right arrow over (s)}. The digital symbols are passed to an RFtransmitter 40 where they undergo pulse-shaping,digital-to-analog-conversion, up-conversion, filtering, andamplification, according to methods well-known in the art, to produce anRF signal. The RF signal is transmitted from transmitter 10 via a singletransmitting antenna 50. The transmitted RF signal passes through amultipath propagation channel and combines with co-channel interferersto form a cumulative RF signal at receiver 20. Co-channel interferenceis illustated in system 1 of FIG. 1 by co-channel transmitter 60 withtransmitting antenna 70. Co-channel transmitter 60 transmits aninterfereing RF signal that occupies the same frequency band as thedesired RF signal from transmitting antenna 50. Co-channel transmitter60 could be, for example, the cellular radio of another user in adistant cell of the same TDMA network. For mathematical simplicity andwithout loss of generality in the description and equations below, weassume only one desired user and one interferer. Furthermore, we assumethat the propagation channels (both for the user and interferer) in theTDMA network are invariant within a TDMA time slot.

Receiver 20 has a plurality of spatially-separated receiving antennas80, which are M in number, for coupling the cumulative RF signal intoreceiver 20 with spatial diversity. The cumulative RF signals coupledthrough antennas 80 then pass through respective analog front ends(AFEs) 90 where they undergo amplification, filtering, down-conversion,and analog-to-digital conversion, according to methods well-known in theart, to produce received signal samples. The received signal samples area discrete-time representation of the received signal (i.e., thedown-converted cumulative RF signal). The received signal sample for thei^(th) AFE 90 at a sampling time k is designated x_(i,k). Forsimplicity, we assume symbol rate sampling (i.e., one received signalsample from each AFE 90 is produced per symbol period), and we expressthe M received signal samples at each time k as an M×1 vector,x_(k)=[x_(1,k). . . x_(M,k)]^(T). Note that the term vector will be usedto refer to column vectors only (i.e., N×1 matricies, where N is apositive integer). Assuming the length of the desired user's channelimpulse response is v+1 samples long, the desired user's channel vectorat the output of the i^(th) AFE 90 is given by h_(i)=[h_(i,0) . . .h_(i,v)]^(T). Similarly, assuming the length of the interferer's channelis u+1 samples long, the interferer's channel vector at the output ofthe i^(th) AFE 90 is given by c_(i)=[c_(i,0) . . . c_(i,u)]^(T). Thereceived signal samples x_(k) include additive white gaussian noisen_(k) (e.g., from AFEs 90). Arranging the desired user's channel vectorsinto an M×(v+1) matrix H and the interferer's channel vectors into anM×(u+1) matrix C, the received signal samples x_(k) are given by:$\begin{matrix}\begin{matrix}{x_{k} = {{\begin{bmatrix}h_{1,0} & \cdots & h_{1,v} \\\vdots & ⋰ & \vdots \\h_{M,0} & \cdots & h_{M,v}\end{bmatrix}\begin{bmatrix}s_{k} \\\vdots \\s_{k - v}\end{bmatrix}} + {\begin{bmatrix}c_{1,0} & \cdots & c_{1,u} \\\vdots & ⋰ & \vdots \\c_{M,0} & \cdots & c_{M,u}\end{bmatrix}\begin{bmatrix}z_{k} \\\vdots \\z_{k - u}\end{bmatrix}} + \begin{bmatrix}n_{1} \\\vdots \\n_{M}\end{bmatrix}}} \\{= {{H \cdot s_{k}} + {C \cdot z_{k}} + {n_{k}.}}}\end{matrix} & (1)\end{matrix}$

In equation (1), s_(k) and z_(k) designate the desired digital datasymbols and the undesired interference (i.e., CCI) symbols at time k,respectively, and s_(k) and z_(k) are (v+1)×1 and (u+1)×1 vectors of thepast v+1 and u+1 data and interference symbols, respectively. Forsimplicity, s_(k) and z_(k) are assumed to be binary with probabilisticexpected values given byE(s_(k)s_(k)^(*)) = σ_(s)²    and  E(z_(k)z_(k)^(*)) = σ_(z)².

For reference, (•)* denotes complex conjugate; (•)^(T) denotestranspose; and (•)^(H) denotes Hermitian.

Equation (1) can be extended to a space-time data model (i.e., Mantennas for spatial diversity and L+1 time taps for temporal diversity)by vertically stacking L+1 taps of x_(k)'s into anM(L + 1) × 1    vector  x_(k) = [x_(k)^(T)⋯  x_(k − L)^(T)]^(T).

The space-time data model is then given by: $\begin{matrix}{{{{\overset{\_}{x}}_{k} = {{\overset{\_}{H} \cdot {\overset{\_}{s}}_{k}} + {\overset{\_}{C} \cdot {\overset{\_}{z}}_{k}} + {\overset{\_}{n}}_{k}}}{where}\quad {{{\overset{\_}{s}}_{k} = \left\lbrack {s_{k}\cdots \quad s_{k - v - L}} \right\rbrack^{T}},{{\overset{\_}{z}}_{k} = \left\lbrack {z_{k}\cdots \quad z_{k - u - L}} \right\rbrack^{T}},{{\overset{\_}{n}}_{k} = \left\lbrack {n_{k}^{T}\cdots \quad n_{k - L}^{T}} \right\rbrack^{T}},}}} & (2) \\{{\overset{\_}{H} = {\begin{bmatrix}H & 0 & \cdots & 0 \\0 & H & \quad & 0 \\\vdots & \quad & ⋰ & \vdots \\0 & 0 & \cdots & H\end{bmatrix}\quad {and}}}} & (3) \\{\overset{\_}{C} = {\begin{bmatrix}C & 0 & \cdots & 0 \\0 & C & \quad & 0 \\\vdots & \quad & ⋰ & \vdots \\0 & 0 & \cdots & C\end{bmatrix}.}} & (4)\end{matrix}$

In equations (3) and (4), 0 are M×1 zero vectors and {overscore (H)} and{overscore (C)} are M(L+1)×(v+L+1) and M(L+1)×(u+L+1) block Toeplitzmatricies, respectively.

The received signal samples x_(k) from AFEs 90 are then passed to adigital receiver 100. In digital receiver 100, the received signalsamples are space-time processed according to the present invention. Foreach symbol time k in a TDMA time slot, digital receiver 100 provides anestimated digital symbol {tilde over (s)} which corresponds to a desireddigital symbol, {right arrow over (s)}, originally transmitted bytransmitter 10. Over an entire TDMA time slot, the individual estimateddigital symbols, {tilde over (s)}, form a sequence of estimated digitalsymbols, {tilde over (s)}, corresponding to the sequence of transmitteddigital symbols, {right arrow over (s)}. The estimated digital symbols,{tilde over (s)}, represent the information signal sent from transmitter10.

A block diagram of a first embodiment of a digital receiver 100according to the present invention is shown in FIG. 2. Digital receiver100 comprises a CCI canceller 120 for suppressing CCI followed an ISIcanceller 130 for suppressing ISI. At each time k, CCI canceller 120processes the received signal samples x_(k), substantially removing itsCCI content to produce CCI-reduced intermediate signal samples y_(k).Intermediate signal samples y_(k) preserve the spatio-temporal structureof the the ISI in x_(k). In other words, intermediate signal y_(k) hassubstantially reduced CCI content and substantially equivalent ISIcontent relative to received signal x_(k). ISI canceller 130 thenprocesses y_(k), substantially removing the ISI and producing anestimated digital symbol {tilde over (s)} for each symbol period (i.e.,at each time k for symbol-rate sampling).

The main component of CCI canceller 120 is a linear filter 140 thatprocesses the received signal x_(k) to produce intermediate signaly_(k). Because we want to keep the spatial information intact such thatISI canceller 130 can make full use of spatial diversity, linear filter140 is implemented as a MIMO space-time filter, typically constructed asan FIR filter as is well-known in the art. Linear filter 140 is anequalizer which performs space-time MMSE processing on the receivedsignal x_(k) to suppress its CCI content according the presentinvention. At each time k, linear filter 140 provides M output samplesy_(i,k) which can be expressed as the vector y_(k)=[y_(1,k) . . .y_(M,k)]^(T). Linear filter 140 has M²(L+1) filter weight coefficients,w_(l,j) ^(i), where i=1,2, . . . , M; I=1,2, . . . , M; and j=1,2, . . ., (L+1). Accordingly, the scalar signal sample Y_(i,k) at the i^(th)output of linear filter 140 is given by: $\begin{matrix}{{y_{i,k} = {{\left\lbrack {w_{i,1}^{T}\quad w_{i,2}^{T}\cdots \quad w_{i,{L + 1}}^{T}} \right\rbrack \begin{bmatrix}x_{k} \\x_{k - 1} \\\vdots \\x_{k - L}\end{bmatrix}} = {w_{i} \cdot {\overset{\_}{x}}_{k}}}}{{{where}\quad w_{i,j}^{T}} = {{\left\lbrack {w_{1,j}^{i}\quad w_{2,j}^{i}\cdots \quad w_{M,j}^{i}} \right\rbrack \quad {and}\quad x_{k}} = {\left\lbrack {x_{1,k}\quad \cdots \quad x_{M,k}} \right\rbrack^{T}.}}}} & (5)\end{matrix}$

A block diagram illustrating the general structure of a two-antenna,three time tap (i.e., M=2, L+1=3) FIR linear filter 140 is shown in FIG.3. Linear filter 140 is comprised of ML delay elements 142, M²(L+1)multipliers 144, and M(M+1) adders 146. Each delay element 142 receivesa signal sample at its input at time k−1 and reproduces the signalsample at its output at time k, delaying the sample by one symbolperiod. Each multiplier 144 receives a signal sample at its input andmultiplies it with a weight coefficient, w_(l,j) ^(i), producing asignal sample at its output which is scaled by the weight coefficient.Each adder 146 receives a plurality of signal samples at its inputs andadds them together, producing a signal sample at its output which is thesum of the input signal samples.

CCI canceller 120 also comprises a channel estimator (i.e., a means forchannel estimation) 150. Channel estimator 150 uses the received signalsamples x_(k) to provide a first set of estimated channel vectors. Thisfirst set of estimated channel vectors (or, alternatively, first channelestimate) comprises a (v+1)×1 estimated channel vector ĥ_(i)=[ĥ_(i,0) .. . ĥ_(i,v)]^(T) for each of the M channels corresponding to the M AFEs90. Channel estimator 150 computes the first set of estimated channelvectors using the least squares technique, which is well-known in theart. CCI canceller 120 further comprises a storage means 160 for storingp+1 training symbols ŝ_(k), ŝ_(k−1), . . . , ŝ_(k−p) and a convolver(i.e., a convolving means) 170 for convolving these training symbolswith the first set of estimated channel vectors from channel estimator150. Lastly, CCI canceller 120 includes a computing means 175 forcalculating the filter weight coefficients according to the presentinvention as described below.

All the elements in digital receiver 100 including delay elements 142,multipliers 144, adders 146, channel estimator 150, storage means 160,convolver 170, and computing means 175 can be implemented by manycircuit and software techniques. These techniques include but are notlimited to dedicated digital signal processing (DSP) firmware andprogrammed general purpose embedded microprocessors. These circuittechniques are well-know in the art, and the specific implementationdetails are not relevant to the present invention. In fact, the entiredigital receiver 100 could be implemented as an algorithm for running ona general purpose microprocessor. In such an implementation, physicaldistinctions between the elements of digital receiver 100 such as themultipliers 144, adders 146 and computing means 175 are not meaningfulexcept to identify specific operations performed by the microprocessoraccording to the method of the present invention. Additionally, thedetails of how the values for the training symbols are obtained is notrelevant to the present invention. For example, the values of thetraining symbols may be permanently stored in storage means 160 (i.e.,storage means 160 can be implemented as a read only memory).Alternatively, the values of the training symbols may be retrieved orcalculated and saved into storage means 160 during system operation.

Using the training symbols, let e_(i) represent an error vector at thei^(th) output of linear filter 140. The error vector e_(i) is given by:$\begin{matrix}{e_{i}^{T} = {{{\left\lbrack {w_{i,1}^{T}\cdots \quad w_{i,{L + 1}}^{T}} \right\rbrack \begin{bmatrix}x_{k} & \cdots & x_{k - p + v} \\x_{k - 1} & \cdots & x_{k - p + v - 1} \\\vdots & ⋰ & \vdots \\x_{k - L} & \cdots & x_{k - p + v - L}\end{bmatrix}} - {\left\lbrack {{\hat{h}}_{i,0}\cdots {\hat{\quad h}}_{i,v}} \right\rbrack \begin{bmatrix}s_{k} & \cdots & s_{k - p + v} \\s_{k - 1} & \cdots & s_{k - p + v - 1} \\\vdots & ⋰ & \vdots \\s_{k - v} & \cdots & s_{k - p}\end{bmatrix}}}\quad = {{w_{i}^{T} \cdot X} - {{\hat{h}}_{i}^{T} \cdot {\hat{S}.}}}}} & (6)\end{matrix}$

Applying deterministic MMSE criterion, we minimize the following costfunction: $\begin{matrix}\begin{matrix}{w_{i}^{T} = {\arg \quad {\min\limits_{w}{e^{i}}^{2}}}} \\{= {{\hat{h}}_{i}^{T} \cdot \hat{S} \cdot {{X^{H}\left( {X \cdot X^{H}} \right)}^{- 1}.}}}\end{matrix} & (7)\end{matrix}$

Equation (7) exists if X is a fat matrix, i.e., if p−v+1 is greater thanM(L+1). CCI canceller 120 satisfies this requirement and uses computingmeans 175 to calculate each w_(i) to obtain the optimal, compositeM×M(L+1) space-time weight vector W=HŜX^(H)(XX^(H))⁻¹ according to thiscriteria. Linear filter 140 uses this weight vector to provide Mintermediate signal samples at its outputs at each time k given by:$\begin{matrix}{y_{k} = {{\begin{bmatrix}w_{1,1}^{T} & \cdots & w_{1,{L + 1}}^{T} \\w_{2,1}^{T} & \cdots & w_{2,{L + 1}}^{T} \\\vdots & ⋰ & \vdots \\w_{M,1}^{T} & \cdots & w_{M,{L + 1}}^{T}\end{bmatrix}\begin{bmatrix}x_{k} \\x_{k - 1} \\\vdots \\x_{k - L}\end{bmatrix}} = {{\begin{bmatrix}w_{1}^{T} \\w_{2}^{T} \\\vdots \\w_{M}^{T}\end{bmatrix} \cdot {\overset{\_}{x}}_{k}} = {W \cdot {\overset{\_}{x}}_{k}}}}} & (8)\end{matrix}$

The error vector e_(i) used in the MMSE formulation above according tothe present invention is different from the error of the conventionalMMSE formulation, which uses training symbols ŝ_(k) as the referencesignal. For example, in a conventional single-stage, MISO space-timeMMSE equalizer, the scalar error e_(k) is given by: $\begin{matrix}{e_{k} = {{\left\lbrack {w_{1}^{T}\cdots \quad w_{L + 1}^{T}} \right\rbrack \begin{bmatrix}x_{k} \\x_{k - 1} \\\vdots \\x_{k - L}\end{bmatrix}} - {\hat{s}}_{k - \Delta}}} & (9)\end{matrix}$

where Δ is the equalizer delay. Hence, a conventional space-time MMSEfilter that minimizes E∥e_(k)∥² simultaneously suppresses ISI and CCI.However, unlike the conventional approach that uses the training symbolsas the reference signal, the present invention uses a filtered versionof the training symbols (i.e., the training symbols convolved with thechannel estimate) as the reference signal. Thus, this reference signalcontains ISI in accordance with the first set of estimated channelvectors, and this assures that the ISI structure and content of x_(k) ispreserved in y_(k) while CCI is suppressed.

The output signal y_(k) from CCI canceller 120 is then passed to ISIcanceller 130 as shown in FIG. 2. ISI canceller 130 comprises a channelestimator 180 and a space-time, multi-channel Viterbi equalizer 190.Channel estimator 180 provides a function much like that of channelestimator 150. It uses the CCI-reduced intermediate signal samples y_(k)to provide a is second set of estimated channel vectors. This second setof estimated channel vectors (or, alternatively, second channelestimate) comprises a (v+1)×1 estimated channel vector ĥ_(i)^(′)=[ĥ_(i,0) . . . ĥ_(i,v) ^(′)]^(T) for each of the M channelscorresponding to the M AFEs 90. Like channel estimator 150, channelestimator 180 computes the second set of estimated channel vectors usingthe least squares technique, which is well-known in the art. However,because channel estimator 180 uses the CCI-reduced signal samples y-hdk, instead of the unprocessed received signal samples x_(k) in itsleast-squares estimation calculations, the second set of estimatedchannel vectors are much more accurate than the first set of estimatedchannel vectors. In other words, the CCI in x_(k) is can mask the ISIstructure of the desired user's channel, causing channel estimator 150to compute an inaccurate first set of estimated channel vectors.However, channel estimator 180 uses y_(k) to compute the second set ofestimated channel vectors. Since y_(k) is substantially free of CCI, thesecond set of estimated channel vectors will be much more accurate thanthe first set of estimated channel vectors. The second set of estimatedchannel vectors are then provided to Viterbi equalizer 190 which usesthese more-accurately estimated channel vectors to process intermediatesignal samples y_(k). Viterbi equalizer 190 substantially removes theISI from y_(k) and provides estimated symbols {tilde over (s)} at itsoutput. Because it determines the estimated symbols using the second setof estimated channel vectors, it can estimate the desired symbols muchmore accurately than prior art receivers which derive a estimatedchannel vectors for their Viterbi equalizers without first removing theCCI from the received signal samples. Viterbi equalizers are well-knownin the art (e.g., see G. E. Bottomley and K. Jamal, “Adaptive Arrays andMLSE Equalization,” 48th IEEE Vehicular Technology Conference, vol. 1,pp. 50-4, 1995.), and the details of the design of Viterbi equalizer 190are not relevant to the present invention.

The first embodiment of the present invention was tested on a GSMscenario with GMSK modulation based on the ETSI standard. Accordingly,there were 26 training symbols ŝ_(k), ŝ_(k−1), ŝ_(k+v−25) (i.e., p+1=26)embedded in the middle of a data burst. With a channel length of v+1taps where (v+1)<[p+2−M(L+1)]=27−M(L+1), the corresponding receivedsignals were

[x _(k) x _(k−1) . . . x _(k−25)]=Ĥ·S+[n _(k) n _(k−1) . . . n_(k−25)]  (10)

where $\begin{matrix}{S = \begin{bmatrix}s_{k} & s_{k - 1} & \cdots & s_{k + v - 25} \\s_{k - 1} & s_{k - 2} & \cdots & s_{k + v - 26} \\\vdots & \vdots & ⋰ & \vdots \\s_{k - v} & s_{k - v - 1} & \cdots & s_{k - 25}\end{bmatrix}} & (11)\end{matrix}$

and H is the same as defined in equation (1). The color noise n_(i)contained CCI and additive white Gaussian noise, and the least squarechannel estimate Ĥ from channel estimator 150 was given by:

Ĥ=[ĥ ₀ . . . ĥ _(v) ]=[x _(k) x _(k−1) . . . x _(k+v−1) ]·S ^(H)(S·S^(H))⁻¹.  (12)

The simulations used the Typical Urban, 50 km/hr mobile velocity (TU50)test model for the multipath fading and delay parameters, as iswell-known in the art. Angle spreads for signals and interferers were 30and 18 degrees, respectively. To simulate an M=2, L=1 space-time digitalreceiver according to the present invention, a two-antenna model wasused along with a 2 time tap space-time CCI canceller 120 and a 2 timetap space-time ISI canceller 130. The signal-to-noise ratio (SNR) wasset at 20 dB for the simulation.

FIG. 4 plots the average raw BER performance for this simulatedtwo-stage digital receiver according to the first embodiment of thepresent invention. The figure also plots the average raw BER performanceof a simulated single-stage space-time Viterbi equalizer and a simulatedsingle-stage space-time MMSE equalizer, both of which simultaneouslyreduce CCI and ISI. Simulations were performed under variouscarrier-to-interference ratios (CIR) in order to evaluate theinterference cancellation capability of the three receivers. The fourth(lowest) curve in FIG. 4 plots the performance of a single-stage Viterbiequalizer in a scenario without CCI. Since a Viterbi equalizer isoptimal for this no-CCI condition, the fourth curve serves as the lowerbound of the BER performance. The gap between the curves of the twosingle-stage approaches and the no-CCI curve illustrates the performancedegradation of single-stage equalizers due to the colored noisecharacteristics and the inaccurate channel estimate caused by CCI. FIG.4 also demonstrates that Viterbi equalizers have better performance thanMMSE equalizers when CIR is high, but MMSE equalizers are more robustwhen CCI is the dominant interference source. However, the two-stagedigital receiver according to the first embodiment of the presentinvention is superior to both single-stage approaches because itsuppresses CCI at the first stage and provides signals with higher CIRfor the second stage. This allows the second stage to determine a moreaccurate channel estimated and perform better ISI equalization. FIG. 4shows that the two-stage digital receiver according to the firstembodiment of the present invention provides increased robustness to CCIand ISI compared to the single-stage approaches even at lowcarrier-to-interference ratios, which are common in both lowfrequency-reuse-factor cellular systems and fixed wireless local-loopsystems.

The structure and operation of a second embodiment of a two-stagedigital receiver 100 according to the present invention will now bediscussed. Like the first embodiment, the second embodiment of digitalreceiver 100 comprises a CCI canceller 120 for reducing the CCI in thereceived signal x_(k) to provide an intermediate signal y_(k) withreduced CCI content and substantially preserved ISI structure. As in thefirst embodiment, CCI canceller 120 is followed by an ISI canceller 130for removing the ISI from the intermediate signal and providingestimated symbols {tilde over (s)}, as shown in FIG. 5.

Unlike the first embodiment of digital receiver 100, however, the secondembodiment uses a hybrid approach consisting of a MISO, space-timelinear filter 200 followed by a single-channel Viterbi equalizer 210.Linear filter 200 is typically constructed as an FIR filter, as iswell-known in the art. A joint optimizer 220 uses the input data x_(k)and the training sequence from a training sequence storage means 230 tojointly determine vectors w_(opt) and h_(opt). Vector w_(opt) is theoptimal vector of filter weight coefficients for MISO space-time linearfilter 200, and h_(opt) is the optimal effective channel vector forsingle-channel Viterbi equalizer 210. Linear filter 200 uses w_(opt) toreduce CCI and maximize SINR. Viterbi equalizer 210 uses the effectivechannel vector h_(opt) to equalize ISI and determine the estimated datasymbols. The influence of CCI on the estimation of the receiverparameters w_(opt) and h_(opt) is reduced by jointly optimizing both thespace-time weight vector w_(opt) and the effective channel vectorh_(opt) by solving a single objective function. The selection of anappropriate objective function for joint optimizer 220 and a techniqueof determining and estimating w_(opt) and h_(opt) according to thepresent invention will now be discussed.

Suppose ŝ_(k-v-L), . . . ŝ_(k+p) is the known training sequence. Usingthe space-time data model in equation (2), the corresponding receivedsignal {overscore (X)}=[{overscore (x)}_(k). . . {overscore (X)}k+p](including the training symbols, CCI, ISI, and noise) can be written as:

{overscore (X)}={overscore (H)}·{overscore (S)}+{overscore(C)}·{overscore (Z)}+{overscore (N)}(13)

where {overscore (S)} is a toeplitz matrix with [s_(k), . . . ,s_(k-v-L)]^(T) and [S_(k), . . . , s_(k+p)] as its first column and row,respectively; {overscore (N)}=[n_(k) . . . n_(k+p)]; and {overscore (Z)}can be constructed similarly to S. Let the intermediate signal samples,y, at the output of the linear filter 200 be:

y ^(T) =w ^(T) {overscore (X)}=h ^(T) {overscore (S)}+e ^(T)  (14)

where w is a M(L+1)×1 vector of the coefficeints of linear filter 200, his the effective channel vector, and e^(T)=w^(T){overscore(X)}−h^(T){overscore (S)} is the error term or disturbance. Thus, theerror term is a difference between the intermediate signal (i.e.,w^(T){overscore (X)} is linear filter 200's output) and a referencesignal containing ISI (i.e., h^(T){overscore (S)} is a reference signalformed by the convolution of the effective channel response with thetraining symbols). The reference signal contains an ISI structureaccording to h. Using the definition SINR=∥h^(T){overscore(S)}∥²/∥e^(T)∥² as the objective function, we set up the following jointoptimization problem: $\begin{matrix}{\max\limits_{w,h}{\frac{{{h^{T}\overset{\_}{S}}}^{2}}{{{{w^{T}\overset{\_}{X}} - {h^{T}\overset{\_}{S}}}}^{2}}.}} & (15)\end{matrix}$

In this joint optimization, w and h are unknown variables, {overscore(X)} are received signals containing the known training sequence, and{overscore (S)} is the training sequence. The technique of separation ofvariables, which is well known in the art, is applied to simplify thejoint optimization in (15). Thus, it is straightforward to change (15)to: $\begin{matrix}\begin{matrix}{h_{opt} = {\arg \quad {\max\limits_{h}\frac{{{h^{T}\overset{\_}{S}}}^{2}}{{{h^{T}{\overset{\_}{S}\left( {{{{\overset{\_}{X}}^{H}\left( {\overset{\_}{X}{\overset{\_}{X}}^{H}} \right)}^{- 1}\overset{\_}{X}} - I} \right)}}}^{2}}}}} \\{= {\arg \quad {\max\limits_{h}\frac{h^{H}\overset{\_}{S}*{\overset{\_}{S}}^{T}h}{h^{H}\overset{\_}{S}*\left( {I - {{{\overset{\_}{X}}^{H}\left( {\overset{\_}{X}{\overset{\_}{X}}^{H}} \right)}^{- 1}\overset{\_}{X}}} \right)*{\overset{\_}{S}}^{T}h}}}} \\{= {\arg \quad {\max\limits_{h}{\frac{h^{H}\overset{\_}{S}*{\overset{\_}{S}}^{T}h}{h^{H}\overset{\_}{S}*P_{{\overset{\_}{X}}^{H}}^{\bot*}{\overset{\_}{S}}^{T}h}.}}}}\end{matrix} & (16)\end{matrix}$

Equation (16) is a generalized eigenvalue problem, and h_(opt) is theeigenvector corresponding to the largest eigenvalue λ_(max) of equation(16) scaled by a non-zero constant, and w_(opt) can be calculated from:

w _(opt) ^(T) =h _(opt) ^(T) {overscore (SX)} ^(H)({overscore (XX)}^(H))⁻¹.  (17)

The weight vector w_(opt) is used by MISO space-time linear filter 200,and h_(opt) is provided to Viterbi equalizer 210 as the effective ISIchannel vector. h_(opt) is jointly optimized with w_(opt) in is equation(15), so no estimation of {overscore (H)} is required, as in the firstembodiment of the present invention.

In this hybrid approach, we choose W_(opt) and h_(opt) such that CCI isminimized by w_(opt) in linear filter 200. The resulting intermediatesignal samples from the output of the space-time linear filter are usedwith the associated effective channel vector h_(opt) to maximize theperformance of single-channel Viterbi equalizer 210. In order tovalidate the objective function for the joint optimizer, we examine thepairwise error probability of the nearest neighbor, which is a dominantand important index of the overall error probability of a Viterbiequalizer. Assume M=1 (i.e., a single antenna case), FIR channel h=[h₀ .. . h_(v)]^(T) for the desired user, and FIR channel c=[c₀ . . .c_(u)]^(T) for the interferer. Both h and c are constant within a TDMAburst and have independent complex Gaussian distributions from one burstto another. A burst of the received signal x=[x₀ . . . x_(N)]^(T) can bewritten as:

x ^(T) =h ^(T) S+c ^(T) Z+n ^(T)  (18)

where S is a toeplitz matrix constructed by the data sequence s=[s_(−v),. . . s_(N)] with [s₀ . . . s_(−v)]^(T) as its first column and [s₀ . .. s_(N)] as its first row; Z is also a toeplitz matrix with [z₀ . . .z_(−u)]^(T) as its first column and [z₀ . . . z_(N)] as its first row;N+1 is the length of the received burst, and n is additive whiteGaussian noise. Suppose a data sequence s is transmitted. An erroneousdecision is made between s and s+Δs when the decision variable D(s, Δs)is less than zero, where D(s, Δs) is defined as:

D(s,Δs)=∥x−(S+ΔS)^(T) h∥ ² −∥x−S ^(T) h∥ ²  (19)

where ΔS is a toeplitz matrix constructed by an admissible errorsequence Δs. Applying the Q-function method, equation (19) simplifiesto:

D(s,Δs)=∥ΔS ^(T) h∥ ²+2Re(h ^(H) ΔS*(Z ^(T) c+n)).  (20)

Given h, c and Z, D(s, Δs) is a Gaussian random variable with mean∥ΔS^(T)h∥²+2Re(h^(H) ΔS*Z ^(T) c) and variance 4h^(H)ΔS*R_(n)ΔS^(T)h,where R_(n)=σ_(n) ²I is the covariance matrix of the real part of thethermal noise and I is the identity matrix. Therefore, the conditionalpairwise error probability P_(e) for a particular burst is:$\begin{matrix}\begin{matrix}{\left. {{{P_{\ominus}\left( {s,{\Delta \quad s}} \right.}h},c,Z} \right) = {\int_{D < 0}{{d_{D{{h,c,Z}}}(D)}\quad {D}}}} \\{= {Q\left( \frac{{{\Delta \quad S^{T}h}}^{2} + {2/{{Re}\left( {h^{H}\Delta \quad S*Z^{T}c} \right)}}}{2\sqrt{h^{H}\Delta \quad S*R_{n}\Delta \quad S^{T}h}} \right)}}\end{matrix} & (21)\end{matrix}$

where Q(•) is defined as${Q(x)} = {\frac{1}{\sqrt{2\pi}}{\int_{x}^{\infty}{{\exp \left( \frac{- y^{2}}{2} \right)}\quad {{y}.}}}}$

Averaging over all possible sequences of Z and across different burstswith respect to c, we obtain: $\begin{matrix}\begin{matrix}{\left. {{P_{\ominus}\left( {s,{\Delta \quad s}} \right.}h} \right) = {\frac{1}{{{No}.\quad {of}}\quad Z}{\sum\limits_{z_{i}}\quad {\int_{c}{P_{\ominus}\quad \left( {s,{\Delta \quad s\left. {h,c,Z} \right)\quad {c}}} \right.}}}}} \\{= {\frac{1}{{{No}.\quad {of}}\quad Z}{\sum\limits_{z_{i}}{Q\left( \frac{{{\Delta \quad S^{T}h}}^{2}}{2\sqrt{h^{H}\Delta \quad S*\left( {{Z_{i}^{T}R_{c}Z_{i}} + R_{n}} \right)\Delta \quad S^{T}h}} \right)}}}}\end{matrix} & (22)\end{matrix}$

where R_(c) is a diagonal matrix with [σ_(c0), . . . , σ_(cu)] as itsdiagonal elements, and σ^(cl) ² is the variance of the real part ofc_(i). Equation (22) can be closely approximated by taking the expectedvalue of Z into the square root of the denominator within theQ-function, and the approximation becomes: $\begin{matrix}{{\left. {{P_{\ominus}\left( {s,{\Delta \quad s}} \right.}h} \right) \approx {Q\left( \frac{{\Delta \quad S^{T}h}}{2\sqrt{\sigma_{n}^{2} + {\sigma_{z}^{2}{\sum\limits_{i = 1}^{u}\quad \sigma_{ci}^{2}}}}} \right)}} = {Q\left( \frac{{\Delta \quad S^{T}h}}{2\sigma} \right)}} & (23)\end{matrix}$

where${\sigma^{2} = {\sigma_{n}^{2} + {\sigma_{z}^{2}{\sum\limits_{i = 1}^{u}\quad \sigma_{ci}^{2}}}}},$

which is the power of the overall disturbance. For the nearest neighbor,particularly in a GSM system, we can choose As to be one bit error(i.e., Δs is all zeros except for one ±2σ_(s) in one of the elements).Therefore the square of the argument inside the Q-function becomes σ_(s)²∥h∥²/σ², or SINR, verifying that this is a reasonable objectivefunction to be maximized, as in equation (21).

A block diagram illustrating the general structure of a two-antenna,three time tap (i.e., M=2, L+1=3) MISO space-time linear filter 200 isshown in FIG. 6. MISO space-time linear filter 200 is comprised ofessentially the same types of elements as MIMO space-time linear filter140. Specifically, MISO space-time linear filter 200 is comprised of MLdelay elements 142, M(L+1) multipliers 144, and one adder 146. As forlinear filter 140 of FIG. 4, the implementation of delay elements 142,multipliers 144, and adders 146 in linear filter 200 can be accomplishedusing many circuit and software techniques which are well-know in theart.

An third embodiment of digtial receiver 100 according to the presentinvention is made by combining elements of the first and secondembodiments described above by replacing MISO linear filter 200 in FIG.5 with a MIMO linear filter 140 and single-channel Viterbi equalizer 210with a multi-channel Viterbi equalizer 190. The filter weight matrixW_(opt) and the channel matrix H_(opt) is then provided by a jointoptimizer 220, as in the second embodiment. To evaluate whether theperformance of digital receiver 100 would improve for this thirdembodiment relative to the second embodiment, consider the use of a MIMOspace-time filter having a weight matrix W with dimension M(L +1)×M anda multi-channel Viterbi equalizer with an effective channel matrix H.The joint optimization problem can be written in a manner similar toequation (15) as: $\begin{matrix}{\max\limits_{W,H}{\frac{{{H^{T}\overset{\_}{S}}}_{F}^{2}}{{{{W^{T}\overset{\_}{X}} - {H^{T}\overset{\_}{S}}}}_{F}^{2}}.}} & (24)\end{matrix}$

Because of the property of Frobenius norm, we can stack each column of Hinto a tall vector {tilde over (h)}, and equation (24) can be rewrittenas: $\begin{matrix}{\max\limits_{\overset{\sim}{h}}\frac{{\overset{\sim}{h}}^{H}D\overset{\sim}{h}}{{\overset{\sim}{h}}^{H}B\overset{\sim}{h}}} & (25)\end{matrix}$

where D and B are M(v+L1)×M(v+L+1) block diagonal matrices with{overscore (S)}*{overscore (S)}^(T) and {overscore(S)}*P_({overscore (X)}) _(^(H)) ^(⊥*){overscore (S)}^(T) as each block,respectively. Since B⁻¹D has M repeated largest eigenvalues, {tilde over(h)} can be any of the corresponding eigenvectors. In any case, the Hreconstructed from f has only one non-zero column vector, which is equalto h_(opt) in equation (16). This shows that the MIMO filter willdegenerate into a MISO filter with weight vector identical to w_(opt) inequation (17). Thus, it shows that although a third embodiment usingMIMO space-time linear filter and multi-channel Viterbi equalizer couldbe used, the use of a MISO space-time linear filter 200 and asingle-channel Viterbi equalizer 210 as in the second embodiment issufficient under the optimization criterion of equation (15).

As mentioned with reference to the first embodiment of the presentinvention, it is well known in the art that a Viterbi equalizer isoptimal only when the input noise is Gaussian and white. However, in thesecond embodiment of a digital receiver according to the presentinvention, neither conditions are met. After the space-time filtering,the intermediate signal y contains desired signal h_(opt){overscore (S)}and disturbance e. When the thermal noise level is low (i.e., high SNR),the residual CCI level in e is still comparable to the noise level andhence it cannot be ignored. Because of the slow Rayleigh fadingassumption, CCI plus noise is not Gaussian distributed within a burst.Instead, it is a combination of a Bernoulli distribution (from CCI datasymbols z_(k)) and a Gaussian distribution (from thermal noise n_(k)).Also, because of the temporal correlation of the CCI and the temporalcoloring from linear filter 200, disturbance e is not white.

One approach to partially alleviate this problem is to use a whiteningfilter prior to the Viterbi equalizer. To justify the use of a temporalwhitening filter in this non-Gaussian environment, again we study thepairwise error probability of the nearest neighbor of a Viterbiequalizer. Using the same notation as in equation (18), single-channelViterbi equalizer 210 makes an erroneous decision when the decisionvariable D(s, Δs) is less than zero, where D(s, Δs) is defined as:$\begin{matrix}{{\begin{matrix}{{D\left( {s,{\Delta \quad s}} \right)} = {{{x - {\left( {S + {\Delta \quad S}} \right)^{T}h}}}^{2} - {{x - {S^{T}h}}}^{2}}} \\{= {{{\Delta \quad S^{T}h} + {Z^{T}c} + {n{^{2}{- {{{Z^{T}c} + n}}^{2}}}}}}} \\{= {p^{H}{Qp}}}\end{matrix}{{{{where}\quad p} = \left\lbrack {h^{T}c^{T}n^{T}} \right\rbrack^{T}},{{and}:}}}} & (26) \\{Q = {\begin{bmatrix}{\Delta \quad S^{*}\Delta \quad S^{T}} & {\Delta \quad S^{*}Z} & {\Delta \quad S^{*}} \\{Z^{H}\Delta \quad S^{*}} & 0 & 0 \\{\Delta \quad S^{T}} & 0 & 0\end{bmatrix}.}} & (27)\end{matrix}$

We derive the pairwise error probability between s and s+Δs conditionedon Z to be: $\begin{matrix}{\left. {{P_{\ominus}\left( {s,{\Delta \quad s}} \right.}Z} \right) = {{\int_{D < 0}{{f_{{D}Z}(D)}\quad {D}}} = {\sum\limits_{\lambda_{i} < 0}\quad {\prod\limits_{\lambda_{i} \neq \lambda_{j}}\quad \frac{1}{1 - \frac{\lambda_{j}}{\lambda_{i}}}}}}} & (28)\end{matrix}$

where λ_(i)'s are eigenvalues of MQ, and M=E(pp^(H)). Finally, we canaverage P_(e) (s,Δs|Z) over all possible sequences of z, whose elementsare i.i.d. Bernoulli random variables, to obtain the pairwise errorprobability of a Viterbi equalizer in the presence of CCI and colorednoise: $\begin{matrix}{{P_{\ominus}\left( {s,{\Delta \quad s}} \right)} = {\frac{1}{{{No}.\quad {of}}\quad Z_{i}}{\sum\limits_{z_{j}}\quad {P_{\ominus}\left( {s,{\Delta \quad s{\left. Z_{i} \right).}}} \right.}}}} & (29)\end{matrix}$

We are interested in knowing whether a temporal whitening filterimproves the performance of single-channel Viterbi equalizer 210 whenthe disturbance Z^(T)c+n is colored, non-Gaussian distributed. Thecovariance matrix R of the disturbance is E(Z^(T)c+n)(Z^(T)c+n)^(H),where the expected value is taken over Z and n since c remains constantwithin a TDMA burst. Therefore, we can apply a whitening filter R^(−½)to x, where R=R^(−½)R^({fraction (H/2)}), and the decision variable D(s,Δs) becomes: $\begin{matrix}{{D\left( {s,{\Delta \quad s}} \right)} = {{{R^{\frac{1}{2}}\left( {x - {\left( {S + {\Delta \quad S}} \right)^{T}h}} \right.}^{2} - {{{R^{\frac{1}{2}}\left( {x - {S^{T}h}} \right.}^{2}.}}}}} & (30)\end{matrix}$

Because R is a function of c, it is difficult to find an analyticalexpression of P_(e) (s, Δs) similar to equations (28) and (29). Thus, weresort to numerical evaluation of the following form: $\begin{matrix}{{P_{\ominus}\left( {s,{\Delta \quad s}} \right)} = {\frac{1}{\text{No. of}\quad Z_{i}}{\sum\limits_{z_{i}}\quad {\int_{h}{\int_{c}{P_{\ominus}\left( {s,{\Delta \quad s\left. {h,c,Z_{i}} \right){{cdh}}\text{where}}} \right.}}}}}} & (31) \\{P_{\ominus}\left( {s,{{\Delta \quad s\left. {h,c,Z_{i}} \right)} = {Q\left( \frac{{{R^{\frac{1}{2}}\Delta \quad S^{T}h}}^{2} + {2{{Re}\left( {h^{H}\Delta \quad S^{*}R^{- 1}Z_{i}^{T}} \right)}c^{2}}}{2\sqrt{h^{H}\Delta \quad S^{*}R^{- 1}R_{n}R^{- 1}\Delta \quad S^{T}h}} \right)}}} \right.} & (32)\end{matrix}$

FIG. 7 shows the pairwise error probability of the nearest neighbor whenΔs is chosen to be all zeros except for one ±2σ_(s) in one of theelements. The comparison demonstrates an approximate 1.5 dB improvementat 10⁻³ error rate when a R^(−½) whitening filter is applied for acolored non-Gaussian disturbance. In a practical situation, thecovariance matrix of the disturbance must be estimated and the length ofthe temporal whitening FIR filter must be limited. Therefore, theexpected benefit form the practical whitening filter would be smallerthan that shown in FIG. 7. In any case, the complexity of single-channelViterbi equalizer 210 grows exponentially with respect to the length ofthe whitening filter, producing a tradeoff between the complexity ofsingle-channel Viterbi equalizer 210 and the gain in BER obtained byapplying the whitening filter in the presence of CCI and noise.

The second embodiment of the present invention was also tested in a GSMscenario with GMSK modulation based on the ETSI standard. Thesimulations used a reduced Typical Urban 6-ray channel model and 50km/hrmobile speed (TU50) for the multipath fading and delay parameters. Onedesired signal and one interferer were assumed to impinge on atwo-element antenna array (i.e., M=2) from random angles within a 120degree sector, each with 30 degree angle spread. The SNR was set at 20dB.

A first simulation determined the raw average BER performance versus CIRof four different digital receiver structures, and the results areplotted in FIG. 8. The first simulated digital receiver was a standardmulti-channel Viterbi equalizer which calculated its branch metricrecursively based on the Euclidean distance between sequences. Thesecond digital receiver was a multi-channel Viterbi equalizer preceededby a spatial whitening filter having a matrix that was derived from thesampled spatial covariance matrix R_(i) of CCI plus noise using theresidue E=X−ĤŜ, where Ĥ is the least squares channel estimate using theknown training symbols Ŝ. When CCI is strong, this digital receiversuffers from an inaccurate R_(i) due to severe channel estimation error.The third and fourth digital receivers were the two-stage digitalreceivers according to the second embodiment of the present inventionwithout noise-whitening filters and with one and two time taps (i.e.,L=0 and L=1), respectively.

FIG. 8 illustrates the substantial improvement in BER of the two-stagereceivers according to the second embodiment of the present inventioncompared to the BER performance the other two receivers. Notice thatthere is a crossover point between the lower two curves. Thisillustrates the tradeoff between the power and the coloring of thedisturbance e. When CCI is strong (i.e., low CIR), a MISO space-timefilter with longer time taps can reduce more disturbance power σ_(e) ².This provides more gain than loss from the coloring of the disturbance.

However, when CCI is weak (i.e., high CIR), the amount of σ_(e) ²reduction by a longer time tap MISO space-time linear filter 200 is notlarge enough to compensate for the coloring it introduces. In any case,if the major concern is a system which suffers from low CIR, such as ina low frequency-reuse-factor system, a MISO space-time linear filter 200with longer time taps provides a good performance over a wide range ofCIR. FIG. 9 demonstrates the use of whitening filters prior to thesingle-channel viterbi equalizers 210 in the two simulated digitalreceivers according to the second embodiment of the present invention.The temporal correlation function R_(e)(k) can be estimated using e inequation (14). Spectral factorization, which is well-known in the art,can be used to obtain a stable and causal whitening filter for thesimulation. Considering the complexity of the Viterbi equalizer, thelength of the FIR whitening filter was limited to 2 taps. As suggestedabove, the whitening filters provide about 1 dB gain at 3% raw averageBER.

The present invention provides a method and apparatus for a two-stage,space-time digital receiver for providing accurately estimated symbolscorresponding to desired symbols from a received signal containing thedesired symbols, CCI, and ISI. Although the invention has been describedunder specific simplified conditions, many extensions to the baselinescheme exist. For example, the invention has been described forconditions including only one desired user and one interferer. However,the method of the present invention could easily be extended to amulti-user, multi-interferer scenario. Additionally, the invention hasbeen described assuming binary-valued symbols. However, the method ofthe present invention could easily be used with other, more complexsymbols. For example, the symbols could be multi-valued forpulse-amplitude modulation (PAM) or complex-valued for quadratureamplitude modulation (QAM). Although additional techniques (such as I-Qprocessing for QAM) would need to be applied, these techniques arewell-known in the art and would not preclude the use of a digitalreceiver according to the present invention. Furthermore, although theinvention has been described for use in a TDMA wireless cellularnetwork, the present invention is very flexible and could be used inmany other packet-based communications applications where the receivedsignal is corrupted by both CCI and ISI, such as wireless local loopsystems.

Many modifications of the embodiments of the digital receiver describedherein are possible without exceeding the scope of the presentinvention, and many of these would be obvious to those skilled in theart. For example, the components of a digital receiver according thepresent invention could be implemented with many circuit and softwaretechniques, including dedicated DSP firmware or general-purposemicroprocessors. In addition, certain details of the present descriptioncan be changed in obvious ways without altering the function or resultsof the essential ideas of the invention. For example, the invention hasbeen described assuming symbol-rate sampling (i.e., one sample per AFEper symbol period). However, the method of the present invention couldeasily be used with over-sampling (i.e., N samples per AFE per symbolperiod, where N is a positive integer). Therefore, although theinvention has been described in connection with particular embodiments,it will be understood that this description is not intended to limit theinvention thereto, but the invention is intended to cover allmodifications and alternative constructions falling within the spiritand scope of the invention as expressed in the appended claims and theirlegal equivalents.

We claim:
 1. In a digital receiver comprising a linear filter and aViterbi equalizer, a method for providing estimated symbolscorresponding to desired symbols from a received signal comprising thedesired symbols, co-channel interference (CCI), and inter-symbolinterference (ISI), the method comprising the steps of: a) coupling thereceived signal through a plurality of spatially-separated antennas tocorresponding inputs of the linear filter; b) passing the receivedsignal through the linear filter to provide an intermediate signal withsubstantially reduced CCI content and substantially equivalent ISIcontent compared to that of the received signal; and c) passing theintermediate signal through the Viterbi equalizer to substantiallyremove the ISI and provide the estimated symbols; wherein the step ofpassing the received signal through the linear filter further comprisesthe steps of: i) determining a first channel estimate from the receivedsignal; ii) convolving known training symbols with the first channelestimate to obtain a reference signal; iii) applying minimum mean-squareerror (MMSE) criteria to the difference between the intermediate signaland the reference signal to compute coefficients for the linear filter;and iv) filtering the received signal in accordance with thecoefficients to produce the intermediate signal.
 2. The method accordingto claim 1 wherein the step of passing the intermediate signal throughthe Viterbi equalizer further comprises the steps of: i) determining asecond channel estimate from the intermediate signal; and ii) Viterbiequalizing the intermediate signal in accordance with the second channelestimate to provide the estimated symbols.
 3. The method according toclaim 2 wherein the step of Viterbi equalizing the intermediate signalis preceded by a step of passing the intermediate signal through atemporal whitening filter.
 4. The method according to claim 3 whereinboth channel estimates are computed using a least squares technique. 5.The method according to claim 1 further comprising the step of jointlydetermining coefficients for both the linear filter and the Viterbiequalizer by maximizing a signal-to-interference-plus-noise ratio (SINR)objective function.
 6. The method according to claim 5 wherein the stepof passing the intermediate signal through the Viterbi equalizer ispreceded by a step of passing the intermediate signal through a temporalwhitening filter.
 7. In a digital receiver comprising a linear filterand a Viterbi equalizer, a method for providing estimated symbolscorresponding to desired symbols from a received signal comprising thedesired symbols, co-channel interference (CCI), and inter-symbolinterference (ISI), the method comprising the steps of: a) providingsamples of the received signal from a plurality of spatially-separatedantennas to respective inputs of the linear filter; b) passing thereceived signal samples through the linear filter to produceintermediate signal samples with substantially reduced CCI content andsubstantially equivalent ISI content compared to that of the receivedsignal samples; and c) passing the intermediate signal samples throughthe Viterbi equalizer to substantially remove the ISI and provide theestimated symbols; wherein the step of passing the received signalsamples through the linear filter further comprises the steps of: i)estimating a first set of estimated channel vectors from the receivedsignal samples; ii) convolving known training symbols with the first setof estimated channel vectors to obtain reference signal samples; iii)applying minimum mean-square error (MMSE) criteria to the differencebetween the intermediate signal samples and the reference signal samplesto compute a weight matrix W of coefficients for the linear filter; andiv) filtering the received signal samples in accordance with W toproduce the intermediate signal samples.
 8. The method according toclaim 7 wherein the linear filter is a multiple-input-multiple-output(MIMO), space-time, finite-impulse-response (FIR) filter.
 9. The methodaccording to claim 8 wherein the step of passing the intermediate signalsamples through the Viterbi equalizer comprises the steps of: i)estimating a second set of estimated channel vectors from theintermediate signal samples; and ii) Viterbi equalizing the intermediatesignal samples in accordance with the second set of estimated channelvectors to provide the estimated symbols.
 10. The method according toclaim 9 wherein the Viterbi equalizer is a multi-channel space-timeViterbi equalizer.
 11. The method according to claim 10 wherein the stepof computing the weight matrix of coefficients is performed by solvingthe equation W=ĤŜX^(H)(XX^(H))⁻¹ where Ĥ is a space-time matrix of thefirst set of estimated channel vectors, Ŝ is a space-time matrix of theknown training symbols, and X is a space-time matrix of the receivedsignal samples.
 12. The method according to claim 11 wherein both setsof estimated channel vectors are computed using a least squarestechnique.
 13. The method according to claim 12 wherein the step ofViterbi equalizing the intermediate signal samples is preceded by a stepof passing the intermediate signal samples through a temporal whiteningfilter.
 14. The method according to claim 12 incorporating symbol-ratesampling.
 15. The method according to claim 7 further comprising a stepof jointly calculating an optimal weight vector w_(opt) and an optimalestimated channel vector h_(opt) such that the intermediate signalsamples satisfy an optimization of an objective function with respect toan error term, wherein the error term is a difference between theintermediate signal samples and reference signal samples containing ISI.16. The method according to claim 15 wherein the step of passing thereceived signal samples through the linear filter comprises the step offiltering the received signal samples in accordance with w_(opt). 17.The method according to claim 16 wherein the step of passing theintermediate signal samples through the Viterbi equalizer comprises thestep of Viterbi equalizing the intermediate signal samples in accordancewith h_(opt).
 18. The method according to claim 17 wherein the linearfilter is a multiple-input-single-output (MISO), space-time,finite-impulse-response (FIR) filter.
 19. The method according to claim18 wherein the Viterbi equalizer is a single-channel Viterbi equalizer.20. The method according to claim 17 wherein the objective function isgiven by: SINR=∥h ^(T) {overscore (S)}∥ ² /e ^(T)∥² =∥h ^(T) {overscore(S)}∥ ² /∥w ^(T) {overscore (X)}−h ^(T) {overscore (S)}∥ ² where e isthe error term, h is an estimated channel vector, {overscore (S)} is aspace-time matrix of known training symbols, {overscore (X)} is aspace-time matrix of the received signal samples, [h^(T){overscore(S)}]^(T) is a vector of the reference signal samples, and[w^(T){overscore (X)}]^(T) is a vector the intermediate signal samples.21. The method according to claim 20 wherein the optimization of theobjective function is described by:$\max\limits_{w,h}\frac{{{h^{T}\overset{\_}{S}}}^{2}}{{{{w^{T}\overset{\_}{X}} - {h^{T}\overset{\_}{S}}}}^{2}}$

such that the resulting w and h are w_(opt) and h_(opt), respectively.